Republican Sen. Rand Paul of Kentucky signalled opposition to the Senate immigration bill after an amendment he authored to strengthen the southern border was killed on the floor last week.

Paul told CNN’s “State of the Union” he will vote against the measure that he says will actually increase the number of illegal border crossings.

“To have a secure border, you have to have a functioning visa work program,” Paul said. “This bill puts new caps and allows less workers in to pick crops, that’s where the illegal immigration is coming from. This bill will actually make that problem worse.”

Republican Sen. Jeff Sessions on Sunday said that a last-minute border security amendment to secure enough conservative votes to pass immigration reform would instead increase unemployment and lower job wages.

“Why would any member of Congress want to vote for a bill at a time of high unemployment and falling wages to bring in a huge surge of new labor that can only hurt the poorest among us the most?” the Alabama lawmaker said on CBS’ “Face the Nation.”

“We’re going to have amnesty first, no enforcement in the future, we’re going to have continued illegality,” Sessions said, citing a report by the Congressional Budget Office.

The same bipartisan office also predicted that with the dramatic increase of legal immigration sanctioned by the bill, the effect would be lower wages and increased unemployment, Sessions said.

Immigration supporters are counting on the so-called border enforcement amendment that will be voted on in the Senate Monday to bring wary conservative Republicans to their side.

But Sessions said the measure falls short of meaningful enforcement and does not fund 20,000-border patrol agents called for by the year 2021.

“It has a specific provision that says [Homeland Security] Secretary [Janet] Napolitano does not have to build any fence if she chooses not to, and she publicly said we have enough fencing,” Sessions said.

“The reason this bill is in trouble, the reason this amendment was thrown here in the last moment, is the promises weren’t fulfilled,” Sessions said.